Inferential Statistics to Analyze Data

Submit the Excel template containing your work. Before submitting your assessment, verify you have included all of the elements listed above.

Note: Be sure to complete Assessment 3 before completing this assessment.

By completing Assessment 3, you are now in the position of having data and summary statistics for your survey.

Use the

Inferential Statistics to Analyze Data Template [XLSX]

to complete this assessment. Review the “Example” sheet in the file first. Then use the corresponding information from Assessment 3 in the “Inferential Statistics” sheet of the template.

For this assessment, analyze data using inferential statistics for your previously defined survey questions. Before you begin your analysis, note the following:

When using the Inferential Statistics to Analyze Data Template, note that there are two pages. Be sure to review each one carefully. The first page is the blank template that you will complete, and the second page is a completed example. Try to model your results on the ones shown.
Enter the sample statistics (proportions and samples sizes for questions 1–4 as well as the sample means, standard deviations, and sample sizes for questions 5–6) in the respective fields of the template. The sample statistics were calculated for each survey question in Assessment 3. Use this prior work to complete this assessment. Note that the sample size must be the same for all six questions.

Calculate a 95% confidence interval for each of your survey questions (1–6). Your final product should have six confidence intervals.
Perform a hypothesis test for each survey question (1–6). Your final product should have six hypothesis tests.

A few notes:

When determining the null and alternative hypotheses for each question, use the typical response values from Assessment 2.
You probably want to write the null hypothesis first. Then, the alternative hypothesis is the opposite of the alternative.
Use the same numerical value for the two hypotheses. You cannot put one value for the null and another for the alternative.
For questions 1–4, we are using the sample proportion to estimate the population proportion. For questions 5–6, we are using the sample mean to estimate the population mean. Thus, we use different formulas for their confidence intervals and for their test statistics in the hypothesis tests.

By successfully completing this assessment, you will demonstrate your proficiency in the following course competencies and rubric criteria:

Competency 3: Derive logical conclusions from inferential statistical procedures.
Compute 95% confidence intervals correctly for multiple variables in a study.
Derive appropriate conclusions based upon calculated confidence intervals for a study.
Choose appropriate hypothesis tests based upon the context of the questions asked.
Specify correct null and alternative hypotheses.
Calculate hypothesis tests correctly for multiple questions in a study.
Derive appropriate conclusions regarding hypotheses according to the results of hypothesis tests.

Inferential Statistics

Your assessment must be submitted using this tem

late. Feel free to add additional work at the bottom, but the top must remain. There are five tables in this worksheet: two for statistical summary, two for confidence intervals, and one for hypothesis tests. To find a table quickly, press Ctrl+G. Press the Tab key to move to input areas of the table.

Note: See the worksheet named “

Example

” (in the bottom tab) for examples of how to fill in the yellow boxes.

Blank row, Table 1 begins in A8.

Statistical

Summary

Question

s 1–4 Confidence Intervals: Questions 1–4 Question Sample Proportion Sample Size

Question

Error Lower Limit Upper Limit Conclusion #1

ERROR:#DIV/0!

ERROR:#DIV/0!
ERROR:#DIV/0!
ERROR:#DIV/0!
#2

#2
ERROR:#DIV/0!
ERROR:#DIV/0!
ERROR:#DIV/0!
ERROR:#DIV/0!
#3

#3
ERROR:#DIV/0!
ERROR:#DIV/0!
ERROR:#DIV/0!
ERROR:#DIV/0!
#4

#4
ERROR:#DIV/0!
ERROR:#DIV/0!
ERROR:#DIV/0!
ERROR:#DIV/0!
End of Table 1, blank row. Table 2 begins in F8. End of Table 2, blank row. Table 3 begins in A15. Statistical Summary: Questions 5–6 Confidence Intervals: Questions 5–6 Question

Sample Mean Sample Std Dev

Sample Size

Question
Error
Lower Limit
Upper Limit
Conclusion
#5

#5
ERROR:#DIV/0!
ERROR:#DIV/0!
ERROR:#DIV/0!
ERROR:#DIV/0!
#6

#6
ERROR:#DIV/0!
ERROR:#DIV/0!
ERROR:#DIV/0!
ERROR:#DIV/0!
End of Table 3, blank row. Table 4 begins in F15. End of table, blank row. Table 5 begins in F21. Blank row. Table 4 begins in F15. End of table, blank row. Table 5 begins in F21. Table 5 begins in F21.

Hypothesis Tests: Questions 1–6

Question

Ho Ha Reject Ho

When Test Statistic Decision

Summary

#1
p
p

ERROR:#DIV/0!

#2
p
p

ERROR:#DIV/0!

#3
p
p

ERROR:#DIV/0!

#4
p
p

ERROR:#DIV/0!

#6
μ
μ

ERROR:#DIV/0!

End of table, blank row.
Rejection criteria: Left-tailed test, reject Ho when

z < -1.645

. Right-tailed test, reject Ho when

z > 1.645

. Two-tailed test, reject Ho when

z < -1.96 or z > 1.96

. End of worksheet.

IMPORTANT:
Be sure you change the population statistic in the Test Statistic formula to reflect what you put in Ho and Ha.

Example

Blank row, Table 1 begins in A8.

Confidence Intervals: Questions 1–4

Question
Sample Proportion
Sample Size

Question
Error
Lower Limit
Upper Limit
Conclusion

5325126

322

5178986

#3
0.48
61

End of Table 1, blank row. Table 2 begins in F8.

End of Table 2, blank row. Table 3 begins in A15.

Statistical Summary: Questions 5–6

Confidence Intervals: Questions 5–6

Question
Sample Mean
Sample Std Dev
Sample Size

Question
Error
Lower Limit
Upper Limit
Conclusion

322

End of Table 3, blank row. Table 4 begins in F15.

End of table, blank row. Table 5 begins in F21.

Blank row. Table 4 begins in F15.

End of table, blank row. Table 5 begins in F21.

Table 5 begins in F21.

Hypothesis Tests: Questions 1–6

Question
Ho
Ha
Reject Ho When
Test Statistic
Decision
Summary

z < -1.645

z > 1.645

Do not Reject Ho

z < -1.645

Reject Ho

z < -1.96 or z > 1.96

Reject Ho

z > 1.645

Reject Ho

End of table, blank row.

Rejection criteria:

End of worksheet.

The work below uses made-up data. Remember that the values you use in your hypotheses are up to you.
You can compare your population parameters to any value; just remember that the sample statistic must agree with your alternate hypothesis.
We always try to reject the null hypothesis; that means we must have evidence (via the sample statistic) that the alternate hypothesis is true.
Click in the cell to see the formula used.
Statistical Summary: Questions 1–4
0.56			322	0.055325126	0.504674874	0.	61	We are 95% confident the true population proportion is between 0.505 and 0.615.
0.43	0.055178986	0.374821014		0.48	We are 95% confident the true population proportion is between 0.375 and 0.485.
0.1279344094	0.3520655906	0.6079344094	We are 95% confident the true population proportion is between 0.352 and 0.608.
0.852	0.0909317885	0.7610682115	0.9429317885	We are 95% confident the true population proportion is between 0.761 and 0.943.
18.7	1.5	0.1671834638	18.5328165362	18.8671834638	We are 95% confident the true population proportion is between 18.533 and 18.867.
492.03	136.62	34.9847970729	457.0452029271	527.0147970729	We are 95% confident the true population proportion is between 457.045 and 527.015.
p ≥ 0.55	p < 0.55	2.1533230134			Do not Reject Ho	There is not sufficient statistical evidence to show the population proportion is less than 0.55.
p ≤ 0.50	p > 0.50	3.009727818	There is not sufficient statistical evidence to show the population proportion is greater than 0.50.
p = 0.60	p ≠ 0.60	z < -1.96 or z > 1.96	-1.913112647	There is not sufficient statistical evidence to show the populaton proportion is not 0.60.
p ≥ 0.75	p < 0.75	1.8397738992	There is sufficient statistical evidence to show the population proportion is less than 0.75.
μ = 17	μ ≠ 17	8.374033941	There is sufficient statistical evidence to show the population mean is not 17.
μ ≤ 119	μ > 119	21.3252630406	There is sufficient statistical evidence to show the population mean is greater than 119.
Left-tailed test, reject Ho when z < -1.645.	Right-tailed test, reject Ho when z > 1.645.	Two-tailed test, reject Ho when z < -1.96 or z > 1.96.

IMPORTANT:
Be sure you change the population statistic in the Test Statistic formula to reflect what you put in Ho and Ha.

Remember that the values used in the hypotheses are whatever you want; just make sure the sample statistic supports Ha.

FORMAT HINT:
Copy the math notation to another cell using copy, then paste. Right-click in the cell to see these options.

>data analysis

0
1
1
6
2

1
1
1
0

0
1
1
1
7
5
0
1
1
1

Mean

047619

0
1
1
0
7
6

058

Standard Error

0
1
1
1
8
4

Median
4

0
0
0
1
4
2

Mode
4

0
0
1
0
6
4

Standard Deviation

0
1
0
0
6
1

Sample Variance

1
1
0
0
4
3

Kurtosis

1
0
1
0
6
5

Skewness

0
1
0
1
3
4

Range
8

0
0
0
0
2
2

Minimum
0

0
0
1
0
5
5

Maximum
8

1
1
1
1
7
4

Sum

1
0
1
1
4
4

Count
84

1
0
0
1
5
3

0
0
1
0
3
6

Smallest(1)
0

0
0
0
1
5
4

Confidence Level(95.0%)

0
1
0
1
5
4

0
0
1
0
1
2
1
0
0
0
4
4
1
0
1
1
5
4
0
0
0
1
3
3
1
0
0
0
5
3
1
0
1
1
3
4
0
1
0
1
3
3
1
1
0
0
4
5
0
0
0
1
3
4
0
0
0
0
3
4
1
1
0
1
10
4
0
0
1
1
5
6
0
0
1
1
4
5
0
1
0
1
7
4
1
1
0
0
2
1
1
1
1
0
4
5
1
0
1
1
4
4
1
0
0
1
3
3
0
1
0
1
5
6
0
1
1
0
5
4
1
1
1
0
7
3
0
0
1
0
3
1
1
0
1
0
2
2
0
0
1
1
6
4
0
0
0
0
5
1
0
0
0
1
6
6
1
0
0
1
3
5
0
1
0
1
5
5

0
1
1
0
7
4
0
1
1
0
7
2

0
1
0
0
6
7
0
0
1
0
4
3

1
0
0
1
1
2

1
0
0
1
4
1

1
1
0
1
6
0
1
0
1
1
4
2

1
0
1
1
3
1

0
0
0
1
1
4
1
1
0
0
4
4
0
0
0
0
1
5
1
0
0
1
6
5

0
0
1
0
2
4

1
1
1
1
8
3

Q2
84

1
1
0
1
8
1

1
0
0
1
6
8

84
0.5476190476
0.4523809524

1
1
0
0
5
0
0
1
0
0
6
3
0
1
1
1
6
4

1
1
0
1
7
2

YES

0
1
1
1
6
3

1
1
0
1
4
2
0
0
0
0
4
2
0
1
1
0
3
4
1
0
1
0
3
7
1
0
0
0
3
2
1
0
0
0
5
4
0
0
0
1
3
1
1
1
0
0
8
0
1
0
1
0
3
5
1
0
1
1
3
2
0
0
1
1
4
0
0
1
1
0
7
1
0
0
0
1
5
2

YES

YES
55%

NO
45%

													Q		1	Q2	Q	3	Q	4	Q	5	Q	6	Sarah Levin
														0
										7	Q6
							8		Mean	4.7142857143	3.36	9
	Standard Error	0.20713					84	0.1884348083
	Median
	Mode
	Standard Deviation	1.8984548478	1.7270335449
	Sample Variance	3.604130809	2.9826448652
	Kurtosis	-0.3187497928	-0.2278284355
	Skewness	0.1738266765	0.0687509261
	Range
	Minimum
	Maximum		10
	Sum	396	283
	Count
	Smallest(1)	Largest(1)
	Confidence Level(95.0%)	0.4119899581
0.3747892548
competence 4
Q5 Histogram (left):
The distribution shows the frequency of different values observed in Q5.
It appears to have a higher concentration around specific values, indicating potential clusters or trends.
Q6 Histogram (right):
The distribution of Q6 values is more spread out, with different peaks.
It may indicate variability in the responses or measurements for Q6.
Question	Sample Size	Yes Proportion	No Proportion
Q1		0.4523809524		0.5476190476
0.4404761905	0.5595238095
Q3	0.4642857143	0.5357142857
Q4
Q1 chart	Q2 chart
			YES		45%	44%
			NO		55%	56%
Q3 chart	Q4 chart
46%
54%

Q1 Chart

Q1 chart YES NO 0.45 0.55000000000000004

Q2 Chart

Q2 chart YES NO 0.44 0.56000000000000005

Q3 Chart

Q3 chart YES NO 0.46 0.54

Q4 Chart

Q4 chart YES NO 0.55000000000000004 0.45

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